A new discrete approximation of the fractional-order operator

Petráš, Ivo

doi:10.1109/carpathiancc.2012.6228705

Cited by 4 publications

(1 citation statement)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Generally, CFE method could In this paper, Equation (10) numerator and denominator polynomials of the digital filter, and p and q are their orders respectively. Without loss of generality, the approximate orders of the numerator and denominator polynomials are set to n (see [20] for more details).…”

Section: Power Series Expansion Of Generating Functionmentioning

confidence: 99%

Discretization of Fractional Order Differentiator and Integrator with Different Fractional Orders

Zhang¹,

Song²,

Zhao³

et al. 2017

ICA

View full text Add to dashboard Cite

This paper is concerned with the discretization of the fractional-order differentiator and integrator, which is the foundation of the digital realization of fractional order controller. Firstly, the parameterized Al-Alaoui transform is presented as a general generating function with one variable parameter, which can be adjusted to obtain the commonly used generating functions (e.g. Euler operator, Tustin operator and Al-Alaoui operator). However, the following simulation results show that the optimal variable parameters are different for different fractional orders. Then the weighted square integral index about the magtitude and phase is defined as the objective functions to achieve the optimal variable parameter for different fractional orders. Finally, the simulation results demonstrate that there are great differences on the optimal variable parameter for differential and integral operators with different fractional orders, which should be attracting more attentions in the design of digital fractional order controller.

show abstract

Section: Power Series Expansion Of Generating Functionmentioning

confidence: 99%